Answer to Question #175711 in Operations Research for Nomi

Question #175711

The Copperfield Mining Company owns two mines, both of which produce three grades of ore— high, medium, and low. The company has a contract to supply a smelting company with at least 12 tons of high-grade ore, 8 tons of medium-grade ore, and 24 tons of low-grade ore. Each mine produces a certain amount of each type of ore each hour it is in operation. Mine 1 produces 6 tons of high-grade, 2 tons of medium-grade, and 4 tons of low-grade ore per hour. Mine 2 produces 2 tons of high-grade, 2 tons of medium-grade, and 12 tons of low-grade ore per hour. It costs $200 per hour to mine each ton of ore from mine 1, and it costs $160 per hour to mine a ton of ore from mine 2. The company wants to determine the number of hours it needs to operate each mine so that contractual obligations can be met at the lowest cost. Formulate a linear programming model for this problem and solve using the simplex method.


1
Expert's answer
2021-05-26T22:29:11-0400

Solution:

Let x = the number of hours that mine 1 operates,

And y = the number of hours that mine 2 operates

Constraint functions are:

"x_1 \\ge0\n\\\\x_2\\ge 0\n\\\\6x_1 + 2x_2 \\ge 12\\Rightarrow 3x_1+x_2\\ge6\n\\\\2x _1+ 2x_2 \\ge8\\Rightarrow x_1+x_2\\ge4\n\\\\4x_1 + 12x_2 \\ge 24\\Rightarrow x_1+3x_2\\ge6"

Minimise cost, "C=200x+160y"

After introducing slack,surplus,artificial variables:



Similarly, doing this process to 6-iteration, we get, optimal solution is arrived with value of variables as :

"x_1=0,x_2=6"

Min Z=$960


Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment

LATEST TUTORIALS
New on Blog
APPROVED BY CLIENTS